Statistical study for ITG turbulent transport in flux-driven tokamak plasmas based on global gyro-kinetic simulation

Flux-driven ion temperature gradient (ITG) turbulence and associated transport regulated by non-local and non-diffusive processes are investigated based on GKNET simulations in a global toroidal geometry. Among these processes, the instantaneous formation of radially extended quasi-coherent structure, which leads to the transport burst, is found to play an important role in causing global profile formation and relaxation. To elucidate the characteristics of such a transport process, we introduce the size probability distribution function (size-PDF) $P\left(S\right)$ to analyze heat flux eddies in the real space, with $S$ the eddy size, incorporated with Fourier-based approaches in spectral space. In the size-PDF to the quiescent phase, $P\left(S\right)$ is found to be fitted by three piecewise power laws which transitions at two typical sizes, $S_a$ and $S_b$, as $P\propto S^{-2/3}\left(S⩽S_a\right)$, $P\propto S^{-2}$ $\left(S_a⩽S⩽S_b\right)$, and $P\propto S^{-4}\left(S⩾S_b\right)$, where $S_a\sim 50$ and $S_b\sim 200$ in squared gyro-radius unit ${\rho }_{\text{i}}^2$ for the system with $a/{\rho }_i\sim 225$ (a: the minor radius). On the other hand, the size-PDF in the bursting phase exhibits non-power-law irregular humps which corresponds to the quasi-coherent structures for $S⩾S_b$ reaching to $S_{max}\sim 1500$. Such a coherent structure is ascribed to the spontaneous alignment of smaller scale eddies through phase matching in radial direction, which is classified as a quasi-deterministic process. Resultantly, a large amount of free energy is extracted from the system due to subsequent growth of the event, by which a self-organized profile is established. The coherent structure is then readily disintegrated by self-generated zonal flows, followed by the energy transferred to smaller eddies. Finally, turbulent transport in the steady state of a flux-driven system is found to be regulated by the mixture of such quasi-deterministic process and probabilistic processes, which leads to stiffness and resilience in the profile formation and self-similarity in the relaxation. (paper)